Question

The distribution of blood cholesterol level in the population of all male patients 20–34 years of age tested in a large hospital over a 10-year period is close to Normal with standard deviation σ = 48 mg/dL (milligrams per deciliter). At your clinic, you measure the blood cholesterol of 14 male patients in that age range. The mean level for these 14 patients is x̄ = 180 mg/dL. Assume that σ is the same as in the general male hospital population. Find a 95% confidence interval for the mean blood cholesterol level of male patients 20–34 years of age at your clinic. a)Does this call for a confidence interval or a hypothesis test? ii) Is this 1 sample or 2 samples? iii) Is this about mean(s) or proportion(s)? iv) If this is about mean(s), do you know the SD of the population (σ — or σ1 & σ2 )? (If this is about proportions, skip this question.) b)What are the population parameter(s), and what are the sample statistic(s)? Provide symbols, and say what they represent in the context of the question. (For example, "µ is the mean completion time of the population, and x̄ is the mean completion time for the sample".) You may want to give the statistic values here. c) if a confidence interval: i) State the confidence level. (If it is not given, make a reasonable choice.) ii) Give the formula for the margin of error (symbols only, no numbers!). iii) Calculate the margin of error (show your work!). iv) State the confidence interval in a complete sentence (in words!), in the context of the original problem. (You may use whichever form you prefer.) d) if hypothesis test: i) State the significance level (alpha). (If it is not given, make a reasonable choice.) ii) Give the formula for the test statistic (z or t) (symbols only, no numbers!). iii) State the null and alternative hypotheses. Use symbols, and state them in the context of the original problem. (A sketch is optional, but very useful.) iv) Calculate the test statistic (z or t) (show your work!), and determine the p-value. v) State your conclusion in a complete sentence (in words!), in the context of the original problem. Your conclusion should state whether or not you reject the null hypothesis, and what this says about the original question.

Answer 1

(a)

(i) This is about a confidence interval

(ii) One-sample

(iii) This is about means

(iv) Yes, σ = 48

(b) n = 14, σ = 4.8, x-bar = 48

(c)

(i) Confidence level = 95%

(ii) Margin of error = Critical z * (σ/√n)

(iii) Margin of error = 1.96 * (48/√14) = 25.1439

(iv) Confidence interval = [180 - 25.1439, 180 + 25.1439] = [154.8561, 205.1439]

We are 95% confident that the true population mean lies in the above interval

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